Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BDE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle ABC \cong \angle DBE$ $, \ $ $ \angle ACB \cong \angle BDE$ $, \ $ $ \overline{AC} \cong \overline{DE}$ $, \ $ $ \angle ECF \cong \angle BDE$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ and $\ $ $ \overline{EF} \cong \overline{BE}$ Proof $ \triangle BDE \cong \triangle FCE$ because AAS $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle BCA$ because AAS $ \overline{BD} \cong \overline{BC}$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle BCE$ because SSS
Explanation: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. There is no wrong statement in this proof.